Knuth's up-arrow notation

The Knuth's up-arrow notation is a notation for large numbers developed
by the American mathematician Donald Knuth (1938–) in 1976. A single
up-arrow ()
is the same as exponentiation:

mn = m × m × ... × m (n terms) = mn

Two up-arrows together represent a power
tower: mn = mm^m^...^m (a tower of height n), which is the same as the operation known
as hyper4 or tetration. This can very rapidly generate huge numbers. For
example:

Even up-arrow notation becomes cumbersome, however, when faced with staggeringly
large numbers such as Graham's number.
For such cases, more extensible systems such as Conway's
chained arrow notation or Steinhaus-Moser notation are better suited. See also the Ackermann
function, to which up-arrow notation is closely related.